Find the Midpoint (8,10) and (5,2)

$(8, 10)$ and $(5, 2)$

Use the midpoint formula to find the midpoint of the line segment.

$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

Substitute in the values for $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

$(\frac{8 + 5}{2}, \frac{10 + 2}{2})$

Add $8$ and $5$ .

$(\frac{13}{2}, \frac{10 + 2}{2})$

Cancel the common factor of $10 + 2$ and $2$ .

Factor $2$ out of $10$ .

$(\frac{13}{2}, \frac{2 \cdot 5 + 2}{2})$

Factor $2$ out of $2$ .

$(\frac{13}{2}, \frac{2 \cdot 5 + 2 \cdot 1}{2})$

Factor $2$ out of $2 \cdot 5 + 2 \cdot 1$ .

$(\frac{13}{2}, \frac{2 \cdot (5 + 1)}{2})$

Cancel the common factors.

Factor $2$ out of $2$ .

$(\frac{13}{2}, \frac{2 \cdot (5 + 1)}{2 (1)})$

Cancel the common factor.

$(\frac{13}{2}, \frac{2 \cdot (5 + 1)}{2 \cdot 1})$

Rewrite the expression.

$(\frac{13}{2}, \frac{5 + 1}{1})$

Divide $5 + 1$ by $1$ .

$(\frac{13}{2}, 5 + 1)$

Add $5$ and $1$ .

$(\frac{13}{2}, 6)$